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The impedance matching section in Bowick is 30 pages long. Half of those pages are full page smith charts.
You won't find a better introduction to lumped element impedance matching anywhere on the planet
---------- Post added at 12:44 ---------- Previous post was at 12:03 ----------
If you want an incredibly crude introduction to basic two element matching then:
Theory:
Every load can be expressed as a single resistance in series with a specific single reactance (at any ONE frequency)
This combination of series resistance + series reactance has a direct equivalent that is a resistance in parallel with a specific single reactance (at the same ONE frequency)
So you have a series signature and a parallel signature that are essentially the same at this target frequency.
Design task: match x to 50 ohms.
If you start with low resistance x and want to match to higher resistance (50 Ohm) then you can do the following:
You shunt the higher resistance (in this case 50 Ohm) with a reactance (both inductive or capacitive reactance will do)
You start off with a very high shunt reactance and adjust it down until the SERIES equivalent of the parallel reactance+50R is equal to x ohms.
When you shunt the 50 Ohm with a reactance you also create (as a side effect) a series equivalent reactance that now needs to be matched out with another reactive component. So you then balance out this SERIES reactance with its opposite reactance to end up with x loaded with x.
This is known as an L match as you use two components to do the match and they are configured as series shunt (an L shape). If you shunt the 50Ohm with a capacitor then you end up with a series inductor to complete the match and vice versa.
Although the circuit looks to us like a L shape, the 'eqivalent' circuit is x looking into a series resonant inductor and capacitor (therefore they cancel to zero) and this is looking into x ohms (you need to keep the theory of the parallel equivalent concept in mind to visualise this)
Bowick will contain all the equations to work this out plus lots of worked examples.
If you want to match 17 Ohm to 50 Ohm at 300MHz then simply shunt the 50 Ohm port with 14.7pF and then add a 12.5nH inductor in series between the 17R port and the 50R port to cancel out the residual series reactance.
This will give a reasonable match over a 100MHz bandwidth. Bowick will explain methods to get higher bandwidths using extra sections.
The simplest network to match 60.95, -45.75 at 300MHz is to shunt the 60.95, -45.75 with a 1.1pF capacitor and then place a 25nH inductor in series between the 50 Ohm port and the load. This is another L match.
The other way to do it is to cancel out the -45.75 with a series 45.75 ohm (24.3nH) from the load and then you just have to match 50 ohm to 60.95 Ohm. You can do this with a regular L match.
So you end up with a series 12.1nH leaving the 50 ohm port, then a shunt 4.0pF followed by the series 24.3nH. This second network will have slightly more bandwidth.
The other way to look at it is to convert 60.95,-45.75 to the parallel equivalent.
This will be 95 ohms in parallel with -126 ohms capactive reactance.
So you could cancl out the -126 ohms using an inductor with reactance of 126 ohm. (67.3nH at 300MHz)
Now you just have to match 95 ohm to 50 ohm.
This can be done with an L match again.
This can be a shunt 52.8nH inductor and a series 11.4pF cap.
But because both inductors are parallel shunt they can be replaced by a single equivalent eg 67.3nH in parallel with 52.8nH is about 30nH.
So the final network is a 30nH inductor across your complex load and a series 11.4pF connecting to the 50 ohm port.
If you get tired of playing with the equations then another intuitive tool is the smith chart matching program by Fritz Dellsperger. I think you can get V3 of this but I am very fond of the older version 1.91.
You simply plot your load impedance on the chart and then navigate the circles of constant resistance or reactance to arrive at the centre of the chart. It draws the network as you navigate.
It really is a very good program and makes an ideal companion to the Bowick book
The simplest network to match 60.95, -45.75 at 300MHz is to shunt the 60.95, -45.75 with a 1.1pF capacitor and then place a 25nH inductor in series between the 50 Ohm port and the load. This is another L match.
The other way to do it is to cancel out the -45.75 with a series 45.75 ohm (24.3nH) from the load and then you just have to match 50 ohm to 60.95 Ohm. You can do this with a regular L match.
So you end up with a series 12.1nH leaving the 50 ohm port, then a shunt 4.0pF followed by the series 24.3nH. This second network will have slightly more bandwidth.
I am now seeing how the elements being in shunt and series move around the Smith Chart. Haven't look at the program yet though.
I appreciate the help and I see that I get a pretty good match with the 3 lumped elements that you stated below. My only issue is that I have a pretty small bandwidth. From the specs I need a pretty small Q. I think it is a Q of 3.
Also not sure how you got those numbers with the second L section to match 50 Ohm to 60.95. Maybe I have to run to the numbers again.
If you could provide a little explanation it would help a lot. Thanks so far though.
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